SOLUTION: The average weight of a box at a store is 10lbs. with a standard deviation of 2 lbs. If 200 boxes are at the store approximately how many boxes will be between 10 and 13 lbs.

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Question 47667: The average weight of a box at a store is 10lbs. with a standard deviation of 2 lbs. If 200 boxes are at the store approximately how many boxes will be between 10 and 13 lbs.
Found 2 solutions by venugopalramana, Nate:
Answer by venugopalramana(3286) (Show Source):
You can put this solution on YOUR website!
The average weight of a box at a store is 10lbs. with a standard deviation of 2 lbs. If 200 boxes are at the store approximately how many boxes will be between 10 and 13 lbs.
10 AND 13 CORRESPOND TO A DEVIATION OF +3 FROM MEAN OF 10 SINCE 13=10+3
DEVIATION OF 3 IS 1.5 TIMES THE STANDARD DEVIATION OF 2 SINCE 2*1.5=3
FROM NORMAL DISTRIBUTION IT IS EXPECTED THAT ABOUT 86% WILL BE BETWEEN -1.5 S.D TO +1.5 S.D AROUND THE MEAN
THAT IS 86% ARE BETWEEN 10-3=7 AND 10+3=13...OR..43% WILL BE BETWEEN 10 AND 13
HENCE APPROXIMATELY 200*43/100=86 BOXES MAY BE BETWEEN 10 AND 13 LBS.

Answer by Nate(3500) (Show Source):
You can put this solution on YOUR website!
sd = standard deviation
average(mean) = m
<--(2%)--(m - 2(sd))--(14%)--(m - sd)--(34%)--(m)--(34%)--(m + sd)--(14%)--(m + 2(sd))--(2%)-->
<--(2%)--(6)--(14%)--(8)--(34%)--(10)--(34%)--(12)--(14%)--(14)--(2%)-->
From 10 to 13 is 1.5 standard deviations: 34% + (1/2)14% = 34% + 7% = 41%
200 boxes * 41% = 82 boxes